On the Kumaraswamy Fisher Snedecor Distribution

We propose the Kumaraswamy-F (KUMAF) distribution which is a generalization of the conventional Fisher Snedecor (F-distribution). The new distribution can be used even when one or more of the regular assumptions are violated. It is obtained with the addition of two shape parameters to a continuous F-distribution which is commonly used to test the null hypothesis in the Analysis of Variance (ANOVA test). The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. The distribution is found to be more flexible and robust to regular assumptions of the conventional F-distribution. In future research, the flexibility of this distribution as well as its robustness using a real data set will be examined. The new distribution is recommended for used in most applications where the assumption underlying the use of conventional F distribution for one-way analysis of variance are violated such as homogeneity of variance or normality assumption probably as result of the presence of outlier(s). It is instructive to note that the new distribution preserves the originality of the data without transformation.